Critical exponents of four-dimensional random-field Ising systems

The ferromagnet-to-paramagnet transition of the four-dimensional random-field Ising model with Gaussian distribution of the random fields is studied. Exact ground states of systems with sizes up to 32(4) are obtained using graph theoretical algorithms. The magnetization, the disconnected susceptibility, the susceptibility, and a specific-heat-like quantity are calculated. Using finite-size scaling techniques, the corresponding critical exponents are obtained: beta=0.13(5), (gamma) over bar =2.83(50), gamma=1.42(20). For the specific heat both alpha=0 (logarithmic divergence) and an algebraic divergence with alpha=0.26(5) are compatible with the data. Furthermore, values for the critical randomness h(c)=4.18(1) and the correlation-length exponent nu=0.78(10) were found. These independently obtained exponents are compatible with all (hyper)scaling relations and support the two-exponent scenario ((gamma) over bar =2gamma).